Mineral Extraction from Mixed Brine Solutions

Abstract

Sulfate minerals (SMs), such as BaSO₄, SrSO₄, and CaSO₄, precipitate when incompatible solutions from the oil industry, such as seawater (SW) and high-salinity brine solutions (HSBSs), are mixed during the oil production process. To investigate the potentiality to extract SM by mixing three different brine solutions, such as HSBS-1, -2, and -3, with SW, at different temperatures and pressures, a practical simple model was used to predict the saturation index (SI), the quantity of precipitated minerals (Y), and the induction time (t_ind) required for precipitation. From the results, it was found that CaSO₄ hemihydrate and SrSO₄ yield lower amounts of precipitate. BaSO₄ precipitation ranges from 20 to 60 mg/L and 1500 mg/L of CaSO₄ anhydrous under ambient conditions. These findings suggest that recovering low-solubility minerals is technically feasible and environmentally preferable to direct disposal.

1. Introduction

Kuwait operates eleven desalination plants to produce potable water with a combined capacity of 683.3 MIGPD (3.106 million m³/day), producing large volumes of brine discharged into the Arabian Gulf. Multi-Stage Flash (MSF) plants typically recover only 10–15% of feedwater as product, rejecting 85–90% as concentrated brine. The total discharge exceeds 3500 MIGPD (MEWRE, 2022) [1]. At the Doha Research Plant Beach Well, brine from reverse osmosis contains 64,800 mg/L of total dissolved solids (TDSs), while brine from the Shuwaikh RO plant reaches 78,500 mg/L. Despite containing high levels of SMs (CaSO₄, SrSO₄, and BaSO₄) and trace metals, these streams are discharged untreated, contributing to environmental stress. Recovering minerals from seawater (SW) and brine solutions of desalination plants (BSDPs) offers a dual benefit: it reduces environmental impact while generating valuable products that can offset costs and increase distilled water output [2,3,4,5,6]. Recent studies also suggest that integrating desalination with chemical or mineral recovery processes improves economic performance and minimizes the risks associated with dumping high-salinity brine directly into the marine environment [7,8,9,10].

1.1. Sulfate Minerals

Sulfate minerals (SMs) such as BaSO₄, SrSO₄, and CaSO₄ form hard, insoluble scales that frequently precipitate in desalination systems and oil production wells. Once formed, they are difficult to remove chemically and cause significant reductions in productivity [11,12,13,14]. In reverse osmosis (RO) systems, sulfate scaling (SS) lowers flux and blocks the membrane’s active layer, often appearing as needle-shaped crystals [15,16,17]. Their adhesion to pipes, filters, and heat exchangers decreases water output, reduces heat transfer efficiency, and increases operation and maintenance costs [18,19,20]. In oil production, sulfate scales typically result from the mixing of incompatible high-salinity brine solutions (HSBSs) with seawater, which promotes rapid precipitation [11,21]. Thus, the main objective of the current study is to determine whether SMs can be extracted in advance, during the pretreatment stage of the desalination process, by mixing seawater with brine water before it enters the desalination equipment. This approach would increase productivity and reduce the risk of scaling in desalination units. Similarly, in oil production wells, removing SMs by precipitating them through mixing with seawater prior to reservoir injection would help prevent scaling inside the reservoir and ultimately enhance well productivity.

1.2. The Economic Value of the Sulfate Minerals

Although sulfate scales are problematic in desalination and oil production, they also represent valuable industrial minerals. High-salinity brine solutions (HSBSs), often mixed with seawater during secondary oil recovery, contain elevated levels of Ba, Sr, and Ca. While mixing is mainly performed to maintain reservoir pressure and reduce costs [22,23,24,25], the resulting precipitation of sulfates yields materials widely used in industry. Gypsum (CaSO₄·2H₂O) is applied in construction, dental products, and food processing; SrSO₄ is essential for specialized glass manufacturing; and barite (BaSO₄) is used in drilling fluids, pigments, X-ray shielding, and medical applications. In 2016, the United States alone consumed 316,000 tons of barite worth USD 37.7 million, primarily from saline sources. By 2025, the price of barite ranged between USD 150 and 186 per ton in Asian markets [26], while by 2023 CaSO₄ and SrSO₄ were sold at approximately USD 868 and USD 800 per ton, respectively, in Asian markets [26]. The global barite market was valued at USD 1.4 billion in 2019 and is projected to reach USD 2.4 billion by 2027, while the gypsum market is expected to surpass USD 2.14 billion by 2025 [27]. These figures illustrate both the economic importance of and growing demand for sulfate minerals. At the same time, their precipitation as hard scales causes operational challenges and economic losses, since mechanical and chemical removal is costly and often ineffective [11,28,29]. This dual character—problematic in industrial operations yet valuable as a raw material—creates opportunities for recovery from brine streams rather than disposal. So, sulfate scales are not only a challenge to be managed but can also represent an opportunity for resource recovery and economic gain in industrial settings.

1.3. Treatment Methods of High Saline Brine Solutions

Brine streams from desalination plants (BSDPs) and high-salinity brine solutions (HSBSs) generated during oil production are among the most complex industrial wastewaters. HSBSs are formed from a mixture of formation water, reservoir water, and injection water, and typically contain very high levels of dissolved salts, inorganic minerals, gases (CO₂, O₂, and H₂S), hydrocarbons, heavy metals, and suspended solids. They also carry toxic organic compounds such as PAHs, BTEX (benzene, toluene, ethylbenzene, and xylene), and NPD (naphthalene, phenanthrene, and dibenzothiophene), as well as treatment chemicals including biocides, corrosion inhibitors, scale inhibitors, and antifoaming agents. Naturally occurring radioactive materials (NORMs) have also been reported in HSBSs [30].

The massive quantity of HSBSs produced in oil production makes the disposal of those streams a global challenge. More than 250 million barrels per day are produced worldwide, nearly three times the volume of crude oil [30,31]. In Kuwait, oil production of 2.41 million barrels/day in 2024 generated about 1.6 million barrels/day of HSBSs [32]. Historically, Kuwait relied on open pits, sealed pits, and reinjection into reservoirs or disposal wells, but these methods are increasingly infeasible due to environmental risks and stricter regulations [33,34].

Conventional treatment of HSBSs involves three stages. Primary treatment includes physical separation methods such as gravity separation (API units), hydrocyclones, and deoiling hydrocyclones, sometimes followed by coagulation-flocculation with agents like bentonite or chitosan and media filtration [30,35]. These methods remove suspended solids, oil droplets, and some metals, with efficiencies up to 90% reported for TSS and metals [36]. Secondary treatment may include clarification, flotation, biological treatment, adsorption, or mineral precipitation [37,38]. Tertiary methods increasingly rely on advanced membranes such as nanofiltration, ultrafiltration, membrane distillation (MD), and membrane crystallization (MCr), as well as advanced oxidation (electrocoagulation, Fenton, and TiO₂/UV photocatalysis), which have achieved > 90% oil removal and significant reductions in COD and TOC [5,39,40,41].

Mineral recovery from HSBSs has been studied since [42] proposed chemical precipitation to reduce disposal costs. Commonly targeted products include NaCl, KCl, CaCO₃, Na₂SO₄, CaSO₄, Mg(OH)₂, BaSO₄, and CaCl₂ [6,43]. Recent advances focus on membrane crystallization, which can achieve the high-purity recovery of salts such as NaCl, CaCO₃, and MgSO₄, and even trace elements like Li, Ba, and Sr at economically significant yields [40,44,45,46]. For example, MCr applied to Kuwait-produced water recovered 37% NaCl, equivalent to 16.4 kg/m³ of high-purity salt [40]. Variants such as antisolvent MCr have demonstrated the selective recovery of minerals at low concentrations, including Ba and Li [47]. Other technologies under investigation include electrodialysis, selective ceramic membranes, and solvent-resistant nanofiltration [29].

The major limitation of membrane processes remains fouling from sparingly soluble salts such as BaSO₄, SrSO₄, CaSO₄, and CaCO₃. For this reason, several researchers have recommended precipitating these minerals prior to desalination, turning scaling elements into valuable products while improving downstream plant efficiency [48,49,50]. In this context, sulfate minerals (SMs) are of particular interest due to their high economic value (

Table 1. The key minerals that could be extracted from mixing HSBSs with SW or BW.

Mineral	Solubility in Water (g/100 mL) @ 20 °C	Ksp @ 25 °C (Approximate)	References
Li2CO3	1.33	5.3 × 10−4	[51]
CaCO3	6.6 × 10−4	3.3 × 10−9 to 8.7 × 10−9	[52]
CaSO4·2H2O	0.21 to 0.27	3.14 × 10−5	[53]
SrSO4	0.0138	3.2 × 10−7	[54]
BaSO4	2.44 × 10−4	1.1 × 10−10	[54,55]
Mg(OH)2	9 × 10−4	1.5 × 10−11	[54,55]
NaCl	35.9	Highly soluble	[56]
KCl	34.4	Highly soluble	[56]
MgCl2	54.3	Highly soluble	[56]
CaCl2	74.5	Highly soluble	[54]
BaCl2	35.7	Highly soluble	[56]

) and low solubility under typical brine conditions. The present study investigates their extraction from mixtures of HSBS, BSDP, and seawater using a modeling approach to predict solubility, induction time, and precipitate yields under different operating conditions.

Table 1 presents the Ksp and solubility of minerals at two temperatures that can be achieved by mixing HSBSs and SW in Kuwait. HSBSs will be hypothetically mixed with SW, and the saturation index (SI) will then be estimated for each type of mineral at different operating parameters.

2. The Calculating Model to Examine the Potential for Extracting SMs from Mixed Solutions

Several models have been developed to predict the behavior of electrolyte solutions resulting from mixing seawater (SW) and high-salinity brine solutions (HSBSs). Early approaches include the Langelier Saturation Index (LSI), the Stiff and Davis model, and the Ryznar Stability Index, while more advanced frameworks are based on the Debye–Hückel theory and the Pitzer model [57].

The LSI is one of the earliest and simplest indices, used to estimate calcium carbonate scaling under ambient pressures and temperatures between 0 and 100 °C. However, it does not account for water alkalinity, hardness, or the effects of high ionic strength. The Stiff and Davis method extended this approach by incorporating ionic strength (up to 4 molality), pH, and TDSs, enabling more reliable predictions for brine and reverse osmosis feedwaters. Nonetheless, it remains limited at molalities above 4 molality, as typically encountered in HSBSs.

The Ryznar Stability Index, proposed in the 1940s, also predicts CaCO₃ scaling potential based on experimental data but does not consider crystallization dynamics or pressure effects. The Puckorius Scaling Index (PSI) improves on these methods by evaluating buffering capacity and estimating the amount of scale needed to reach equilibrium.

For highly concentrated and mixed electrolyte systems, the Pitzer model provides the most robust framework. Developed in the 1970s and refined in the 1990s [57,58,59], it calculates activity coefficients for multi-component solutions using the Debye–Hückel equation, Gibbs free energy functions, and molality expansions. The model accounts for ionic interactions, charge effects, and the influence of temperature and pressure, enabling the accurate prediction of solubility products (Ksp), saturation ratios (Qs), and mean activity coefficients up to ionic strengths of 8 molality. Its main limitation is the reliance on extensive empirical parameters and mathematically complex formulations to capture cation–anion interactions [58]. The governing equations are summarized in Equations (1)–(5) (below):

K_{sp (MX)} = (a _M²⁺)·(a _X²⁻) = γ₊ [M²⁺] γ₋ [X²⁻]

(1)

a: activity, γ: activity coefficient.

[M²⁺]: molar concentration of species M in the target solution in mol solute (dissolved species or ion)/kg of brine water.

[X]: molar concentration of species or ion X in a kg of brine solution.

The Pitzer model for the activity coefficients of ions in the absence of neutral species is given as below [60]:

ln (γ_i) = f ^γ + ∑_i ∑_j m_im_jB_ij + ∑_i ∑_j ∑_k m_i m_j m_k C_ijk

(2)

f _γ: Debye–Hückel term count for long-term interaction, Bij: coefficient related to the binary interaction of all components (plus–minus, plus–plus, and minus–minus), and Cijk: the ternary interaction of all ions (plus–minus–plus, plus–minus–minus, and minus–plus–plus).

(γ_M) = Z_M² f ^γ + ∑_c ∑_a m_cm_aB′ _ca + ∑_c ∑_c′ m_cm_c′ϕ′_cc′ + ∑_a ∑_a′ m_am_a′ϕ′_aa′ + ∑_a m_a (2B_Ma + Ec_Ma) + ∑_c m_c (2ϕ_Mc + ∑_a m_a ψ_Mca) + |Z_M|*I*∑_c ∑_a m_c m_a C_ca + ∑_a ∑ _a′ ψ_Maa′

(3)

a: anion, c: cation, γ_M: ionic activity of cation or anion, Z_M: charge of species M, E: equivalent molality, m_a: molality of anion, m_c: molality of cation, ψ and ϕ: electrochemical interaction terms, I: ionic strength, T: temperature in kelvin, and P: pressure in psia.

E = ∑_i|Z_i|m_i
f ^γ = A_ϕ {[I^(0.5)/(1 + 1.2*I^(0.5)]+ [ (2/1.2)*ln{ 1 + 1.2*I^(0.5)}]

(4)

A_ϕ is determined from [61] as a function of temperature.

A_ϕ = 3.3690153 × 10⁻¹ − 6.3210043 × 10⁻⁴T + 9.14252359/T − 1.35143986 × 10⁻²ln(T) + 2.26089488 × 10⁻³/{T − 263} + 1.921185973 × 10⁻⁶T² + 4.52586464E1/(680 − T)

(5)

Simões et al. [62] examined the Pitzer model for pure electrolytes at 25 °C and introduced new parameters that eliminated the need for empirical data while maintaining predictive accuracy. Monnin et al. [63] developed a model based on the measured solubility data of sulfate minerals in NaCl solutions, using solution density to estimate molal concentrations. Their approach involved plotting the solubility data for salts such as KCl, NaCl, CaCl₂, Na₂SO₄, and MgCl₂ at 25 °C. Odd et al. [64,65] proposed a model to calculate the saturation index (SI) of sulfates and carbonates at temperatures of 35–80 °C and pressures up to 3500 psi. Their model introduced the conditional solubility product (Kco) to simplify SI and Ksp estimation but showed high deviations due to neglecting crystallization kinetics. Ulfsbo et al. [60] later improved accuracy by applying charged hard-sphere and Monte Carlo approaches to calculate activity coefficients, requiring fewer parameters. Results from the Alfsbo model confirmed agreement with Pitzer predictions for CaSO₄ under operating conditions. Jian [20] contributed experimental solubility data, showing that BaSO₄ solubility decreases with increasing ionic strength but increases with temperature.

In Kuwait, Al-Bazali [66] evaluated the Debye–Hückel screening length (κ⁻¹) to estimate diffusion layer thickness in high-ionic-strength produced water, demonstrating its impact on the swelling and shrinking of NaCl, KCl, and CaCl₂ salts. Correa et al. [28] reviewed the experimental solubility limits of SS under high temperature and pressure, emphasizing that HSBS compositions differ significantly from seawater. Their work with the extended UNIQUAC model showed that CaCl₂ and MgCl₂ increase SS solubility, while Na₂SO₄ reduces it via the common ion effect. Correa also highlighted the lack of multi-component solubility data for realistic HSBS conditions (50–300 bar). Gamal et al. [13] analyzed scale deposits from Saudi oilfields, reporting almost pure BaSO₄ (97.7–100%) as the dominant precipitate. They proposed chelating agents such as DTPA, tannic acid, and oxalic acid as effective dissolution treatments, achieving up to 76.9% removal at 35 °C and 91.3% at 90 °C, with significant recovery of reservoir permeability.

Alongside empirical models, several software packages are widely used. UNIQUAC [67] and ScaleChem (developed by Oli-system Inc., 2108 American Road Morris Plains) predict scaling potential through iterative calculations of brine composition, and both have been refined to improve reliability [68,69]. PHREEQC, developed by the US Geological Survey, is now the most widely applied program, capable of handling complex solution chemistry and used in membrane distillation crystallization studies for NaCl, sulfate minerals, and Mg(OH)₂ recovery [4,28].

Moghadasi et al. [70] proposed an alternative model for SS and CaCO₃ scaling at ionic strengths up to 12 M, based on simplified calculations derived from earlier solubility data [71,72,73,74]. The model calculates activity coefficients using a conditional constant (Kco) and compares the ion product (IP) with Ksp to estimate SI under variable temperature, pressure, and ionic strength [75]. More recently, Samira et al. [76] applied a similar framework to Iranian oilfield brines, using mixing ratios of seawater and HSBSs to determine mineral concentrations and predict scaling. The concentration of minerals in both models was estimated based on the amount of seawater mixed with HSBSs, as shown in Equation (6). The main limitation of the proposed model is that it is confined to ionic strengths up to 12 molarity and uses Kco as a simplified assumption for calculating activity coefficients in mixed brine solutions. The model assumes homogeneous mixing with consistent temperature and pressure throughout the system. Furthermore, it does not account for the kinetic effects of nucleation or the influence of organic and inorganic additives commonly found in oilfield waters. Despite this, the model proposed by Moghadasi et al. [70] has demonstrated reliable performance in predicting the potential for mineral precipitation when oil-produced water is mixed with seawater or brine water. It effectively estimates scaling tendencies, particularly for sulfate and carbonate scales, under various mixing ratios and physicochemical conditions typical of oilfield waters. The model’s predictions have been validated and applied successfully in several studies addressing Iranian oilfield brines and other reservoir conditions involving seawater injection and produced water mixing [76].

SI = Log [M][X] + pKsp (T, P, I)
Q_S(MX) = [M²⁺] _brine * [X²⁻] _brine

(6)

Saturation index (SI) = log ([ M²⁺] [X²⁻] + pK_sp)

(7)

Ksp = [M − Y] [X − Y]

Rearranged Equation (6) to Equation (7):

Y² − (M + X) Y + M·X − Ksp = 0

(8)

where [X²⁺] is the concentration in molar units (mol/L), and Ksp is a function of ionic strength, pressure, and temperature. Y is the amount of MX precipitated when the SI is above zero. When the SI is less than zero, the mineral is not expected to precipitate, while precipitation is expected when the SI is greater than zero. The primary challenge in estimating the scaling potential in highly concentrated brine solutions, as evident from the proposed models, is calculating the saturation indices for SMs as a function of temperature, pressure, and ionic strength, particularly in the high ionic strength of the resulting mixed solutions.

Three methods can be used to estimate the scaling potential of minerals in highly concentrated brine solutions. The first method involves experimental work to measure the actual solubility of the minerals in these brine solutions. The saturation indices will then be calculated using Ksp, Qs, and SI. The second method relies on the use of the Pitzer method. Then, the activity coefficient (ai) of the required ions can be calculated, and based on this, all the saturation constants and indices can be determined as a function of ionic strength, temperature, and pressure. The third method utilizes experimental data to estimate the reaction’s conditional constant (Kco) as a function of temperature, pressure, and ionic strength. The advantage of using experimental data is that the activities of the cation and anion of the interested minerals do not need to be determined by Pitzer’s complicated equations, but are instead included in the conditional constants (Kco), which are determined from real data, as in the Maghadasi model and the Odd and Tomas model. This method is preferred by many researchers and was employed in our calculations to estimate the SM potential in high-brine solutions, as explained below. The required data for the SS can also be found in literature data or [64,65]. The equation proposed to calculate the Kco or (K_st) as a function of temperature, pressure, and (I) is shown in Equation (9):

Log K_co = 1.86 + 4.5 × 10⁻³T − 1.2 × 10⁻⁶T^² + 10.7 × 10⁻⁵P − 2.38(I^^0.5) + 0.58(I^^0.5) − 1.3 × 10⁻³(I^^0.5) T

(9)

where P is the pressure in psi, T is the temperature in K, and C is the concentration in mol of solute/kg solvent (molality). Then, the total or summation of neutral ion pairs as CaSO₄°, which dissolved or complexed in the mixed solution [Sum (C_SO4)], was calculated from the K_co as shown in Equations (10)–(12). Details of the model were available in [70].

C_SO4 = [CaSO₄°] + [BaSO₄°] + [SrSO₄°] + [MgSO₄°] + [SO₄°]

(10)

SUM (C_SO4) = (C_Ba − Cso₄) + (C_Ca − C_SO4) + (C_Sr- C_SO4) + (C_Mg − C_SO4)

(11)

Then [SO₄²⁻] = [−1{1 + Kco(SUM) + {1 + Kco(SUM)^² + 4Kco C_SO4}^^0.5]/2K_co

(12)

Next, the mass balance equations for total dissolved SMs were calculated from Equations (13)–(15):

[Ba²⁺] = C_Ba/(1 + {K_co [SO₄²⁻]})

(13)

[Sr²⁺] = C_sr/(1 + {K_co [SO₄²⁻]})

(14)

[Ca²⁺] = C_ca/(1 + {K_co [SO₄²⁻]})

(15)

Then, the Ksp and SI for each SM will be calculated as below:

Ksp(BaSO₄) = 10.03 − 4.8 × 10⁻³T + 11.4 × 10⁻⁵T^² − 4.8 × 10⁻⁵P − 2.62I^^0.5 + 0.89I − 2.0 × 10⁻³ I^^0.5T

(16)

Ksp(CaSO₄.2H₂O) = 3.47 − 1.8 × 10⁻³T + 2.5 × 10⁻⁶T^² − 5.9 × 10⁻⁵P − 1.13I^^0.5 + 0.37I − 2.0 × 10⁻³I^^0.5T

(17)

Ksp(SrSO₄) = 6.11 − 2.0 × 10⁻³T + 6.4 × 10⁻⁵T^² − 4.6 × 10⁻⁵P − 1.8I^^0.5 + 0.6I − 1.9 × 10⁻³I^^0.5T

(18)

SI (_MSO4) = LOG ([C_M] [C_SO4]) + Ksp _(MSO4) (T, P, I)

(19)

Then, the mixing ratio is plotted versus the SI for high-brine solutions, for brine water or seawater.

In regard to induction time, an empirical model was proposed by Kan and Masson (2012) [77] and was supported by other researchers [78], depending on the T and SI and incorporating the interfacial tension constant (C) for SM scaling, as shown in Equation (20) [77] calculated the induction time for scaling minerals like CaSO₄, SrSO₄, and BaSO₄ based on classical nucleation theory, using Equation (20):

$${\mathrm{t}}_{\mathrm{ind}} = \mathrm{C}·(\mathrm{lnSI}{)}^{-2}·{\mathrm{T}}^{-3}$$

(20)

where ${\mathrm{t}}_{\mathrm{ind}}$ is the induction time (sec), $\mathrm{SI}$ is the saturation index,$\mathrm{T}$ is the temperature (K), and C is the constant.

3. Result and Discussion

3.1. Analysis of Water Samples Collected

Seawater samples were collected from the intake of the Doha East Desalination Plant, while three HSBS samples were obtained from different oil production facilities in Kuwait over a two-month period, once per week. Sampling followed international QA/QC standards [79] to ensure accuracy, precision, and representativeness. Written standard operating procedures (SOPs) governed collection, preservation, transport, and storage, as well as equipment calibration and analytical performance. QA/QC also included the use of check standards to confirm system stability, blanks to correct for reagent and processing effects, and certified reference materials (CRMs) to verify methodology.

Composite seawater samples were prepared weekly by combining grab samples from multiple intake locations into polyethylene containers. Field measurements of pH, residual chlorine, temperature, and turbidity were taken immediately after collection. All containers were stored in ice and transported to the laboratory within three hours. Chemical samples were filtered to remove turbidity and analyzed without delay.

Analyses included major ions and cations dissolved in seawater and HSBSs. Alkalinity (HCO₃⁻ and CO₃²⁻) was measured by automatic titration [80]. Sodium, potassium, magnesium (Mg²⁺), and calcium (Ca²⁺) were determined by ion chromatography (ICS-5000, Dionex, Sunnyvale, CA, USA) following [81]. Chloride and sulfate were analyzed according to SMEWW 4110B, while barium and strontium were quantified by ICP-OES (ICP-ES-6200) in compliance with [82], with a detection limit of 2 µg/L for barium. Calibration solutions were prepared from certified standards with similar ionic matrices to seawater and HSBSs to reduce interferences. Linearity was verified using regression analysis of calibration curves. Internal standards, CRMs, blanks, spikes, and duplicates were employed to ensure accuracy and precision.

Results were processed to calculate average (AVG), maximum (MAX), minimum (MIN), standard deviation (SDEV), and relative standard deviation (RSD). Data from seawater at Doha East (

Table 2. Chemical composition of Kuwait seawater at the intake of the Doha East Desalination Plant.

Parameters	AVG	MAX	MIN	STDEV	RSD
SW	Doha East	Doha East	Doha East	Doha East	Doha East
pH	7.70	8.10	7.50	0.21	2.74
TDS	48,529	49,200	48,020	419.77	0.86
HCO3−	130.0	132.0	128.6	1.09	0.83
Na+	16,352	16,945	15,850	323.11	1.97
K+	586	620	540	24.05	4.10
Mg2+	1536	1700	1450	71.44	4.65
Ca2+	1029	1200	970	54.69	5.31
Cl−	25,207	26,500	24,450	592.82	2.35
Sr2+	13.2	14.5	12.3	0.708	5.34
Ba2+	0.007	0.008	0.006	0.0005	6.65
SO42−	3815	4000	3649	77.4	2.02

) and HSBS samples HSBS-1, HSBS-2, and HSBS-3 from oil production sites (

Table 3. Chemical analysis of the HSBS-3-19 stream from oil production in Kuwait.

	PH	TDS	HCO3−	Na+	K+	Mg2+	Ca2+	Cl−	SO42−	Ba2+	Sr2+	NO3−	F−
		mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L
AVG	6.4	175,793	213.5	63,557	2180	1924	9232	98,000	175	30.2	360	16.2	4.5
MAX	6.8	182,600	225.5	66,085	2500	2010	9450	99,150	180	31.2	410	17.5	5.3
MIN	6.2	173,800	205.8	60,339	1900	1850	9140	95,760	165	29.6	320	15.2	3.8
STDEV	0.1	2893	5.1	1148	170	37	83	730	3.9	0.4	19	0.7	0.4
RSD	2.2	2.0	2.4	1.8	7.8	1.9	0.9	0.7	2.2	1.2	5.3	4.1	9.2
SEM	0.03	631.00	1.10	250.6	37.20	8.00	18.0	159.40	0.9	0.08	4.10	0.10	0.10
U (95%)	0.1	1263	2.2	501	74	16	36	319	1.7	0.2	8	0.3	0.2
CI upper	6.5	177,056	215.7	64,058	2255	1940	9268	98,318	176	30.4	368	16.5	4.7
CI lower	6.3	174,530	211.3	63,056	2106	1908	9196	97,681	173.4	30.0	352	15.9	4.3

,

Table 4. Chemical analysis of the HSBS-2-17 stream from oil production in Kuwait.

	PH	TDS	HCO3−	Na+	K+	Mg2+	Ca2+	Cl−	SO42−	Ba2+	Sr2+	NO3−	F−
		mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L
AVG	6.3	243,212	183	96,923	5085	2720	9156	149,400	328	49.1	653	34	4.0
MAX	6.6	248,300	185	97,650	5250	2780	9590	150,400	340	50.2	680	43	4.4
MIN	5.6	240,100	181	96,100	4950	2680	9000	148,600	300	47.2	620	32	3.7
STDEV	0.24	1805.67	1.19	482.03	72.50	27.61	125.0	473.3	10.3	0.6	15.3	2.8	0.2
RSD	3.76	0.74	0.65	0.50	1.43	1.02	1.36	0.32	3.1	1.3	2.34	8.21	4.5
SEM	0.05	394.03	0.26	105.19	15.82	6.03	27.27	103.28	2.3	0.14	3.33	0.61	0.04
U (95%)	0.10	788.06	0.52	210.38	31.64	12.05	54.54	206.56	4.6	0.3	6.67	1.22	0.1
CI upper	6.4	244,000	183.5	97,134	5117	2732	9211	149,607	332.3	49.4	660	35	4.1
CI lower	6.2	242,424	182.5	96,713	5054	2708	9102	149,193	323.0	48.8	647	33	3.9

and

Table 5. Chemical analysis of the HSBS-1-15 stream from oil production in Kuwait.

	pH	TDS	HCO3−	Na+	K+	Mg2+	Ca2+	Cl−	SO42−	Ba2+	Sr2+	NO3−	F−
		mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L
AVG	5.6	197,999	171	83,299	2620	2715	9603	128,400	610.25	82.31	400.00	10.98	4.10
MAX	6.0	199,869	173	83,810	2710	2760	9680	130,800	630.00	84.10	450.00	12.10	4.50
MIN	5.5	195,899	169	82,800	2560	2680	9550	125,900	580.00	80.50	370.00	9.50	3.80
STDEV	0.13	860.43	0.93	266.36	32.23	23.82	30.50	967.99	12.82	0.84	23.66	0.57	0.17
RSD	2.349	0.43	0.54	0.32	1.23	0.88	0.32	0.75	2.10	1.02	5.92	5.15	4.26
SEM	0.029	187.76	0.20	58.12	7.03	5.20	6.66	211.23	2.87	0.19	5.16	0.12	0.04
U (95%)	0.058	375.52	0.40	116.25	14.07	10.40	13.31	422.47	5.73	0.37	10.33	0.25	0.08
CI upper	5.7	198,375	171	83,416	2634	2725	9616	128,823	615.98	82.68	410.33	11.23	4.17
CI lower	5.6	197,624	170	83,183	2606	2705	9590	127,978	604.52	81.94	389.67	10.73	4.02

) were then used as inputs for the proposed model. This model predicts the precipitation or extraction of sulfate minerals when HSBSs are mixed with Kuwait seawater at varying temperatures and pressures, including the quantity of precipitated minerals and induction times.

3.2. The Chemical Composition of HSBSs and Doha East SW

The chemical analysis showed that HSBS-2-17 has the highest TDS (243,212 mg/L), indicating extreme salinity, and is slightly acidic due to its low pH. In contrast, HSBS-2-17 and HSBS-3-19 are closer to neutral, with pH values of 6.4 and 6.3, respectively. HSBS-1-15 contains the highest average concentrations of barium (82.31 mg/L), calcium (9603 mg/L), and sulfate (610.25 mg/L), suggesting a strong tendency to precipitate CaSO₄ and BaSO₄. HSBS-2-17, however, has the highest strontium concentration (653 mg/L).

Kuwait seawater (SW) itself contains a high sulfate concentration, reaching 3815 mg/L, compared to only 610 mg/L in HSBS-1-15. The concentrations of barium and strontium in HSBS-1-15 are 82 times and 600 times higher, respectively, than in Kuwait SW. Calcium in HSBS-1-15 is also more than nine times higher than in seawater. While Ba and Sr levels in Kuwait SW are relatively low (≤0.007 and 13.2 mg/L), the much higher sulfate content of SW means that mixing it with HSBSs increases the overall sulfate concentration as the proportion of seawater rises. At the same time, the concentrations of Ba and Sr decrease with dilution, creating favorable conditions for the precipitation of BaSO₄, CaSO₄, and SrSO₄. Since sulfate mineral (SM) precipitation depends primarily on sulfate concentration rather than cation concentration, higher SW fractions increase both the saturation index (SI) and the likelihood of SM precipitation (Table 2, Table 3, Table 4 and Table 5).

Significant differences between Kuwait SW and HSBSs are also evident in bicarbonate, calcium, and pH, which promote additional scaling. For example, mixing can raise the pH to around 8.3, leading to calcite (CaCO₃) precipitation, and at a pH above 9.5 Mg(OH)₂ precipitation is likely. These chemical contrasts are the main cause of incompatibility between SW and HSBSs, driving SM precipitation. The low RSD values reported confirm the consistency and reliability of the analyses.

The relatively low pH of HSBSs, despite high bicarbonate concentrations, is likely linked to elevated dissolved CO₂ and organic acids produced by microbial hydrocarbon degradation. Dissolved CO₂, common in reservoirs, shifts bicarbonate equilibria toward hydrogen ion formation, lowering pH despite abundant HCO₃⁻. Sulfate-reducing bacteria also contribute by producing H₂S under high-sulfate conditions. Other factors such as reservoir age, depth, and temperature further influence HSBS chemistry and acidity.

3.3. The Saturation Index of SMs in Mixed Solutions

The chemical composition of Doha East seawater was incorporated into the model and mixed with three types of HSBSs (HSBS-1, HSBS-2, and HSBS-3) at varying ratios. A constant volume of each HSBS sample was used, while the seawater fraction was gradually increased from 0 to 100%. The composition of the mixed streams was calculated in mg/L using the mass balance equation (Equation (A1), Appendix B) based on the specified mixing ratios; the calculation results for BaSO₄ mixed with HSBS-3-19 are presented in

Table A1. Chemical composition of the mixed solution (SW and HSBS-1-19).

Mixing Ratio	Volume	Total Volume	Volume	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L	mg/L
%	SW	After Mixing of HSBS	HSBS	CO32−	HCO3−	Na+	K+	Mg2+	Ca2+	Cl−	SO42−	Ba2+	Sr2+
0	0.00	1.00	1.00	0.00	214	63,577	2180	1924	9232	98,000	175	30	360
5	0.05	1.05	1.00	0.00	210	61,328	2104	1906	8841	94,534	348	29	343
10	0.10	1.10	1.00	0.00	206	59,284	2035	1889	8486	91,383	506	27	328
15	0.15	1.15	1.00	0.00	203	57,417	1972	1873	8162	88,505	650	26	315
20	0.20	1.20	1.00	0.00	200	55,706	1915	1859	7865	85,868	782	25	302
25	0.25	1.25	1.00	0.00	197	54,132	1862	1846	7592	83,442	903	24	291
30	0.30	1.30	1.00	0.00	194	52,679	1813	1834	7339	81,202	1015	23	280
35	0.35	1.35	1.00	0.00	192	51,334	1768	1823	7106	79,128	1119	22	270
40	0.40	1.40	1.00	0.00	190	50,084	1725	1813	6889	77,202	1215	22	261
45	0.45	1.45	1.00	0.00	188	48,921	1686	1804	6687	75,409	1305	21	252
50	0.50	1.50	1.00	0.00	186	47,836	1650	1795	6498	73,736	1388	20	244
55	0.55	1.55	1.00	0.00	184	46,820	1615	1786	6322	72,171	1467	19	237
60	0.60	1.60	1.00	0.00	182	45,868	1583	1779	6156	70,703	1540	19	230
65	0.65	1.65	1.00	0.00	181	44,974	1553	1771	6001	69,324	1609	18	223
70	0.70	1.70	1.00	0.00	179	44,132	1525	1764	5855	68,027	1674	18	217
75	0.75	1.75	1.00	0.00	178	43,338	1498	1758	5717	66,803	1735	17	211
80	0.80	1.80	1.00	0.00	176	42,589	1473	1752	5587	65,648	1793	17	206
85	0.85	1.85	1.00	0.00	175	41,879	1449	1746	5464	64,555	1847	16	201
90	0.90	1.90	1.00	0.00	174	41,208	1426	1740	5347	63,520	1899	16	196
95	0.95	1.95	1.00	0.00	173	40,570	1405	1735	5236	62,537	1948	15	191
100	1.00	2.00	1.00	0.00	172	39,965	1385	1730	5131	61,604	1995	15	187

, Appendix B. Subsequently, the concentration was converted to mol/L, with the results shown in

Table A2. Chemical composition of the mixed solution in mol/liter.

mol/L	mol/L	mol/L	mol/L	mol/L	mol/L	mol/L	mol/L	mol/L
HCO3−	Na+	K+	Mg2+	Ca2+	Cl−	SO42−	Ba2+	Sr2+
0.003500	2.764217	5.45 × 10−2	7.91 × 10−2	2.30 × 10−1	2.76	1.82 × 10−3	2.20 × 10−4	4.11 × 10−3
0.003435	2.666445	5.26 × 10−2	7.84 × 10−2	2.21 × 10−1	2.67	3.62 × 10−3	2.09 × 10−4	3.92 × 10−3
0.003376	2.577561	5.09 × 10−2	7.77 × 10−2	2.12 × 10−1	2.58	5.26 × 10−3	2.00 × 10−4	3.75 × 10−3
0.003321	2.496406	4.93 × 10−2	7.71 × 10−2	2.04 × 10−1	2.50	6.76 × 10−3	1.91 × 10−4	3.59 × 10−3
0.003272	2.422014	4.79 × 10−2	7.65 × 10−2	1.96 × 10−1	2.42	8.13 × 10−3	1.83 × 10−4	3.45 × 10−3
0.003226	2.353574	4.65 × 10−2	7.60 × 10−2	1.89 × 10−1	2.35	9.40 × 10−3	1.76 × 10−4	3.32 × 10−3
0.003184	2.290398	4.53 × 10−2	7.55 × 10−2	1.83 × 10−1	2.29	1.06 × 10−2	1.69 × 10−4	3.19 × 10−3
0.003145	2.231902	4.42 × 10−2	7.50 × 10−2	1.77 × 10−1	2.23	1.16 × 10−2	1.63 × 10−4	3.08 × 10−3
0.003109	2.177584	4.31 × 10−2	7.46 × 10−2	1.72 × 10−1	2.18	1.26 × 10−2	1.57 × 10−4	2.98 × 10−3
0.003075	2.127012	4.22 × 10−2	7.42 × 10−2	1.67 × 10−1	2.13	1.36 × 10−2	1.52 × 10−4	2.88 × 10−3
0.003044	2.079812	4.12 × 10−2	7.38 × 10−2	1.62 × 10−1	2.08	1.44 × 10−2	1.47 × 10−4	2.79 × 10−3
0.003014	2.035656	4.04 × 10−2	7.35 × 10−2	1.58 × 10−1	2.04	1.53 × 10−2	1.42 × 10−4	2.70 × 10−3
0.002987	1.994261	3.96 × 10−2	7.32 × 10−2	1.54 × 10−1	1.99	1.60 × 10−2	1.37 × 10−4	2.62 × 10−3
0.002961	1.955374	3.88 × 10−2	7.29 × 10−2	1.50 × 10−1	1.96	1.67 × 10−2	1.33 × 10−4	2.55 × 10−3
0.002936	1.918775	3.81 × 10−2	7.26 × 10−2	1.46 × 10−1	1.92	1.74 × 10−2	1.29 × 10−4	2.48 × 10−3
0.002913	1.884267	3.75 × 10−2	7.23 × 10−2	1.43 × 10−1	1.88	1.81 × 10−2	1.26 × 10−4	2.41 × 10−3
0.002892	1.851676	3.68 × 10−2	7.21 × 10−2	1.39 × 10−1	1.85	1.87 × 10−2	1.22 × 10−4	2.35 × 10−3
0.002871	1.820847	3.62 × 10−2	7.18 × 10−2	1.36 × 10−1	1.82	1.92 × 10−2	1.19 × 10−4	2.29 × 10−3
0.002852	1.791641	3.57 × 10−2	7.16 × 10−2	1.33 × 10−1	1.79	1.98 × 10−2	1.16 × 10−4	2.23 × 10−3
0.002833	1.763932	3.51 × 10−2	7.14 × 10−2	1.31 × 10−1	1.76	2.03 × 10−2	1.13 × 10−4	2.18 × 10−3
0.002816	1.737609	3.46 × 10−2	7.12 × 10−2	1.28 × 10−1	1.74	2.08 × 10−2	1.10 × 10−4	2.13 × 10−3

, Appendix B. Then, the ionic strength at different mixing ratios was calculated using Equation (A2) in Appendix B, and the results for the BaSO₄–HSBS-3-19 mixture are shown in

Table A3. Calculation of the ionic strength of the mixed solution at different mixing ratios.

MLIf*Z^4	MLIf*Z^1	ML*Z^2	ML*Z^2	MLIf*Z^1	ML*Z^2	ML*Z^2	ML*Z^2	SUM(Mli*Z^2)	Ionic Strength (Mixture)
Na+	K+	Mg2+	Ca2+	Cl−	SO42−	Ba2+	Sr2+	Sum (ion.Z^Equivalence)	0.5 *SUM
3.35	6.61 × 10−2	3.84 × 10−1	1.12	3.35	8.84 × 10−3	1.07 × 10−3	1.99 × 10−2	8.31	4.15
3.21	6.34 × 10−2	3.78 × 10−1	1.06	3.21	1.75 × 10−2	1.01 × 10−3	1.89 × 10−2	7.97	3.98
3.08	6.09 × 10−2	3.72 × 10−1	1.01	3.08	2.52 × 10−2	9.57 × 10−4	1.79 × 10−2	7.66	3.83
2.97	5.86 × 10−2	3.67 × 10−1	9.69 × 10−1	2.97	3.22 × 10−2	9.10 × 10−4	1.71 × 10−2	7.39	3.69
2.86	5.66 × 10−2	3.62 × 10−1	9.28 × 10−1	2.86	3.85 × 10−2	8.67 × 10−4	1.63 × 10−2	7.14	3.57
2.77	5.48 × 10−2	3.58 × 10−1	8.92 × 10−1	2.77	4.42 × 10−2	8.28 × 10−4	1.56 × 10−2	6.91	3.45
2.68	5.31 × 10−2	3.54 × 10−1	8.58 × 10−1	2.68	4.95 × 10−2	7.93 × 10−4	1.50 × 10−2	6.70	3.35
2.60	5.15 × 10−2	3.50 × 10−1	8.27 × 10−1	2.60	5.43 × 10−2	7.60 × 10−4	1.44 × 10−2	6.51	3.25
2.53	5.01 × 10−2	3.47 × 10−1	7.99 × 10−1	2.53	5.88 × 10−2	7.30 × 10−4	1.38 × 10−2	6.33	3.17
2.46	4.88 × 10−2	3.44 × 10−1	7.73 × 10−1	2.46	6.29 × 10−2	7.02 × 10−4	1.33 × 10−2	6.17	3.09
2.40	4.76 × 10−2	3.41 × 10−1	7.48 × 10−1	2.40	6.67 × 10−2	6.77 × 10−4	1.29 × 10−2	6.02	3.01
2.34	4.65 × 10−2	3.38 × 10−1	7.26 × 10−1	2.34	7.02 × 10−2	6.53 × 10−4	1.24 × 10−2	5.88	2.94
2.29	4.54 × 10−2	3.36 × 10−1	7.05 × 10−1	2.29	7.35 × 10−2	6.31 × 10−4	1.20 × 10−2	5.75	2.87
2.24	4.44 × 10−2	3.33 × 10−1	6.85 × 10−1	2.24	7.66 × 10−2	6.10 × 10−4	1.17 × 10−2	5.63	2.81
2.19	4.35 × 10−2	3.31 × 10−1	6.67 × 10−1	2.19	7.95 × 10−2	5.90 × 10−4	1.13 × 10−2	5.51	2.76
2.14	4.26 × 10−2	3.29 × 10−1	6.49 × 10−1	2.14	8.22 × 10−2	5.72 × 10−4	1.10 × 10−2	5.41	2.70
2.10	4.18 × 10−2	3.27 × 10−1	6.33 × 10−1	2.10	8.47 × 10−2	5.55 × 10−4	1.07 × 10−2	5.31	2.65
2.06	4.10 × 10−2	3.25 × 10−1	6.18 × 10−1	2.06	8.71 × 10−2	5.39 × 10−4	1.04 × 10−2	5.21	2.61
2.03	4.03 × 10−2	3.24 × 10−1	6.03 × 10−1	2.03	8.94 × 10−2	5.24 × 10−4	1.01 × 10−2	5.12	2.56
1.99	3.96 × 10−2	3.22 × 10−1	5.90 × 10−1	1.99	9.15 × 10−2	5.09 × 10−4	9.84 × 10−3	5.04	2.52
1.96	3.90 × 10−2	3.21 × 10−1	5.77 × 10−1	1.96	9.35 × 10−2	4.96 × 10−4	9.59 × 10−3	4.96	2.48

, Appendix B. Equations (6)–(19) were applied to estimate the saturation index (SI) of five sulfate minerals (SMs) in the mixed solutions [65,70]. A sample of calculations for BaSO₄ mixed with HSBS-3-19 is shown in

Table A4. Calculation of K_co based on temperature (C) and pressure in psia at different mixing ratios.

Pressure	Pressure	Temp.	Temp.
Psia	Bar	C	K	C1	C2	C3	C4	i^0.5	C6	C7	C8	log Kco	Kco
2.668 × 10−4	2.209 × 10−3	4.984 × 10−3	2.794 × 10−1	9.601 × 10−2	−1.942 × 10−3	2.775 × 10−3	2.772 × 10−1	0.093804	3.719 × 10−1	1.609 × 10−2
2.522 × 10−4	4.365 × 10−3	4.721 × 10−3	2.657 × 10−1	9.440 × 10−2	−4.113 × 10−3	3.557 × 10−4	2.613 × 10−1	0.090033	3.476 × 10−1	1.861 × 10−2
2.392 × 10−4	6.298 × 10−3	4.485 × 10−3	2.533 × 10−1	9.295 × 10−2	−6.059 × 10−3	−1.813 × 10−3	2.470 × 10−1	0.086653	3.258 × 10−1	2.120 × 10−2
2.274 × 10−4	8.041 × 10−3	4.272 × 10−3	2.422 × 10−1	9.165 × 10−2	−7.814 × 10−3	−3.769 × 10−3	2.341 × 10−1	0.083605	3.062 × 10−1	2.383 × 10−2
2.168 × 10−4	9.620 × 10−3	4.079 × 10−3	2.321 × 10−1	9.046 × 10−2	−9.404 × 10−3	−5.542 × 10−3	2.225 × 10−1	0.080842	2.884 × 10−1	2.648 × 10−2
2.071 × 10−4	1.106 × 10−2	3.903 × 10−3	2.229 × 10−1	8.939 × 10−2	−1.085 × 10−2	−7.155 × 10−3	2.119 × 10−1	0.078328	2.722 × 10−1	2.913 × 10−2
1.982 × 10−4	1.237 × 10−2	3.743 × 10−3	2.145 × 10−1	8.840 × 10−2	−1.217 × 10−2	−8.631 × 10−3	2.021 × 10−1	0.076028	2.574 × 10−1	3.175 × 10−2
1.900 × 10−4	1.358 × 10−2	3.595 × 10−3	2.068 × 10−1	8.750 × 10−2	−1.339 × 10−2	−9.985 × 10−3	1.932 × 10−1	0.073918	2.438 × 10−1	3.432 × 10−2
1.825 × 10−4	1.469 × 10−2	3.459 × 10−3	1.997 × 10−1	8.667 × 10−2	−1.451 × 10−2	−1.123 × 10−2	1.850 × 10−1	0.071974	2.313 × 10−1	3.685 × 10−2
1.756 × 10−4	1.572 × 10−2	3.334 × 10−3	1.932 × 10−1	8.590 × 10−2	−1.554 × 10−2	−1.238 × 10−2	1.774 × 10−1	0.070179	2.197 × 10−1	3.930 × 10−2
1.692 × 10−4	1.667 × 10−2	3.218 × 10−3	1.871 × 10−1	8.518 × 10−2	−1.650 × 10−2	−1.345 × 10−2	1.704 × 10−1	0.068514	2.090 × 10−1	4.167 × 10−2
1.632 × 10−4	1.755 × 10−2	3.110 × 10−3	1.814 × 10−1	8.452 × 10−2	−1.739 × 10−2	−1.444 × 10−2	1.639 × 10−1	0.066967	1.990 × 10−1	4.395 × 10−2
1.577 × 10−4	1.838 × 10−2	3.009 × 10−3	1.762 × 10−1	8.390 × 10−2	−1.822 × 10−2	−1.537 × 10−2	1.578 × 10−1	0.065525	1.897 × 10−1	4.614 × 10−2
1.525 × 10−4	1.915 × 10−2	2.915 × 10−3	1.712 × 10−1	8.333 × 10−2	−1.900 × 10−2	−1.623 × 10−2	1.521 × 10−1	0.064179	1.810 × 10−1	4.823 × 10−2
1.476 × 10−4	1.987 × 10−2	2.827 × 10−3	1.666 × 10−1	8.279 × 10−2	−1.972 × 10−2	−1.704 × 10−2	1.468 × 10−1	0.062918	1.729 × 10−1	5.021 × 10−2
1.430 × 10−4	2.055 × 10−2	2.744 × 10−3	1.623 × 10−1	8.228 × 10−2	−2.040 × 10−2	−1.780 × 10−2	1.418 × 10−1	0.061736	1.653 × 10−1	5.207 × 10−2
1.387 × 10−4	2.118 × 10−2	2.666 × 10−3	1.583 × 10−1	8.181 × 10−2	−2.104 × 10−2	−1.851 × 10−2	1.371 × 10−1	0.060624	1.581 × 10−1	5.383 × 10−2
1.347 × 10−4	2.178 × 10−2	2.593 × 10−3	1.544 × 10−1	8.136 × 10−2	−2.164 × 10−2	−1.919 × 10−2	1.327 × 10−1	0.059577	1.514 × 10−1	5.547 × 10−2
1.309 × 10−4	2.234 × 10−2	2.524 × 10−3	1.508 × 10−1	8.093 × 10−2	−2.221 × 10−2	−1.982 × 10−2	1.285 × 10−1	0.058590	1.450 × 10−1	5.699 × 10−2
1.273 × 10−4	2.288 × 10−2	2.459 × 10−3	1.474 × 10−1	8.053 × 10−2	−2.275 × 10−2	−2.042 × 10−2	1.245 × 10−1	0.057657	1.390 × 10−1	5.840 × 10−2
1.239 × 10−4	2.338 × 10−2	2.397 × 10−3	1.442 × 10−1	8.016 × 10−2	−2.326 × 10−2	−2.099 × 10−2	1.208 × 10−1	0.056774	1.333 × 10−1	5.969 × 10−2

,

Table A5. Calculation of free sulfate ions and the summation of all neutral ion pairs, Sum(C_M-C_SO4).

C Ba2+	C SO42−	C Sr2+	C Ca2+	C Mg2+	Ba2+-SO42−	Sr2+-SO42−	Ca2+-SO42−	Mg2+-SO42−	Sum (M-SO42−)	Kco*(M-SO42−)
2.668 × 10−4	2.209 × 10−3	4.984 × 10−3	2.794 × 10−1	9.601 × 10−2	−1.942 × 10−3	2.775 × 10−3	2.772 × 10−1	0.093804	3.719 × 10−1	1.609 × 10−2
2.522 × 10−4	4.365 × 10−3	4.721 × 10−3	2.657 × 10−1	9.440 × 10−2	−4.113 × 10−3	3.557 × 10−4	2.613 × 10−1	0.090033	3.476 × 10−1	1.861 × 10−2
2.392 × 10−4	6.298 × 10−3	4.485 × 10−3	2.533 × 10−1	9.295 × 10−2	−6.059 × 10−3	−1.813 × 10−3	2.470 × 10−1	0.086653	3.258 × 10−1	2.120 × 10−2
2.274 × 10−4	8.041 × 10−3	4.272 × 10−3	2.422 × 10−1	9.165 × 10−2	−7.814 × 10−3	−3.769 × 10−3	2.341 × 10−1	0.083605	3.062 × 10−1	2.383 × 10−2
2.168 × 10−4	9.620 × 10−3	4.079 × 10−3	2.321 × 10−1	9.046 × 10−2	−9.404 × 10−3	−5.542 × 10−3	2.225 × 10−1	0.080842	2.884 × 10−1	2.648 × 10−2
2.071 × 10−4	1.106 × 10−2	3.903 × 10−3	2.229 × 10−1	8.939 × 10−2	−1.085 × 10−2	−7.155 × 10−3	2.119 × 10−1	0.078328	2.722 × 10−1	2.913 × 10−2
1.982 × 10−4	1.237 × 10−2	3.743 × 10−3	2.145 × 10−1	8.840 × 10−2	−1.217 × 10−2	−8.631 × 10−3	2.021 × 10−1	0.076028	2.574 × 10−1	3.175 × 10−2
1.900 × 10−4	1.358 × 10−2	3.595 × 10−3	2.068 × 10−1	8.750 × 10−2	−1.339 × 10−2	−9.985 × 10−3	1.932 × 10−1	0.073918	2.438 × 10−1	3.432 × 10−2
1.825 × 10−4	1.469 × 10−2	3.459 × 10−3	1.997 × 10−1	8.667 × 10−2	−1.451 × 10−2	−1.123 × 10−2	1.850 × 10−1	0.071974	2.313 × 10−1	3.685 × 10−2
1.756 × 10−4	1.572 × 10−2	3.334 × 10−3	1.932 × 10−1	8.590 × 10−2	−1.554 × 10−2	−1.238 × 10−2	1.774 × 10−1	0.070179	2.197 × 10−1	3.930 × 10−2
1.692 × 10−4	1.667 × 10−2	3.218 × 10−3	1.871 × 10−1	8.518 × 10−2	−1.650 × 10−2	−1.345 × 10−2	1.704 × 10−1	0.068514	2.090 × 10−1	4.167 × 10−2
1.632 × 10−4	1.755 × 10−2	3.110 × 10−3	1.814 × 10−1	8.452 × 10−2	−1.739 × 10−2	−1.444 × 10−2	1.639 × 10−1	0.066967	1.990 × 10−1	4.395 × 10−2
1.577 × 10−4	1.838 × 10−2	3.009 × 10−3	1.762 × 10−1	8.390 × 10−2	−1.822 × 10−2	−1.537 × 10−2	1.578 × 10−1	0.065525	1.897 × 10−1	4.614 × 10−2
1.525 × 10−4	1.915 × 10−2	2.915 × 10−3	1.712 × 10−1	8.333 × 10−2	−1.900 × 10−2	−1.623 × 10−2	1.521 × 10−1	0.064179	1.810 × 10−1	4.823 × 10−2
1.476 × 10−4	1.987 × 10−2	2.827 × 10−3	1.666 × 10−1	8.279 × 10−2	−1.972 × 10−2	−1.704 × 10−2	1.468 × 10−1	0.062918	1.729 × 10−1	5.021 × 10−2
1.430 × 10−4	2.055 × 10−2	2.744 × 10−3	1.623 × 10−1	8.228 × 10−2	−2.040 × 10−2	−1.780 × 10−2	1.418 × 10−1	0.061736	1.653 × 10−1	5.207 × 10−2
1.387 × 10−4	2.118 × 10−2	2.666 × 10−3	1.583 × 10−1	8.181 × 10−2	−2.104 × 10−2	−1.851 × 10−2	1.371 × 10−1	0.060624	1.581 × 10−1	5.383 × 10−2
1.347 × 10−4	2.178 × 10−2	2.593 × 10−3	1.544 × 10−1	8.136 × 10−2	−2.164 × 10−2	−1.919 × 10−2	1.327 × 10−1	0.059577	1.514 × 10−1	5.547 × 10−2
1.309 × 10−4	2.234 × 10−2	2.524 × 10−3	1.508 × 10−1	8.093 × 10−2	−2.221 × 10−2	−1.982 × 10−2	1.285 × 10−1	0.058590	1.450 × 10−1	5.699 × 10−2
1.273 × 10−4	2.288 × 10−2	2.459 × 10−3	1.474 × 10−1	8.053 × 10−2	−2.275 × 10−2	−2.042 × 10−2	1.245 × 10−1	0.057657	1.390 × 10−1	5.840 × 10−2
1.239 × 10−4	2.338 × 10−2	2.397 × 10−3	1.442 × 10−1	8.016 × 10−2	−2.326 × 10−2	−2.099 × 10−2	1.208 × 10−1	0.056774	1.333 × 10−1	5.969 × 10−2

,

Table A6. Mass balance calculation using the calculated K_co and ∑ (C_M-C_SO4) to estimate [SO₄²⁻] at equilibrium.

∑(M-Cso4)	B	C1	C2	C3	C4	C5	C6	At Equilibrium
sum∑ (M-SO42−)	Kco*(∑(M-SO42−))	Kco* ((∑M-SO42−)^2)	Kco*C SO42−*4	1.000	2.000	3.000	2^0.5	[SO42−]
3.719 × 10−1	1.609 × 10−2	5.985 × 10−3	3.825 × 10−4	−1.016	1.032	1.016	0.000	2.174 × 10−3
3.476 × 10−1	1.861 × 10−2	6.470 × 10−3	9.352 × 10−4	−1.019	1.038	1.019	0.000	4.284 × 10−3
3.258 × 10−1	2.120 × 10−2	6.908 × 10−3	1.640 × 10−3	−1.021	1.043	1.022	0.001	6.165 × 10−3
3.062 × 10−1	2.383 × 10−2	7.297 × 10−3	2.504 × 10−3	−1.024	1.048	1.025	0.001	7.849 × 10−3
2.884 × 10−1	2.648 × 10−2	7.637 × 10−3	3.534 × 10−3	−1.026	1.054	1.028	0.002	9.364 × 10−3
2.722 × 10−1	2.913 × 10−2	7.927 × 10−3	4.734 × 10−3	−1.029	1.059	1.031	0.002	1.073 × 10−2
2.574 × 10−1	3.175 × 10−2	8.170 × 10−3	6.105 × 10−3	−1.032	1.064	1.035	0.003	1.198 × 10−2
2.438 × 10−1	3.432 × 10−2	8.367 × 10−3	7.648 × 10−3	−1.034	1.070	1.038	0.004	1.311 × 10−2
2.313 × 10−1	3.685 × 10−2	8.521 × 10−3	9.363 × 10−3	−1.037	1.075	1.041	0.005	1.414 × 10−2
2.197 × 10−1	3.930 × 10−2	8.633 × 10−3	1.125 × 10−2	−1.039	1.080	1.045	0.005	1.508 × 10−2
2.090 × 10−1	4.167 × 10−2	8.708 × 10−3	1.330 × 10−2	−1.042	1.085	1.048	0.006	1.595 × 10−2
1.990 × 10−1	4.395 × 10−2	8.747 × 10−3	1.551 × 10−2	−1.044	1.090	1.051	0.007	1.676 × 10−2
1.897 × 10−1	4.614 × 10−2	8.754 × 10−3	1.788 × 10−2	−1.046	1.094	1.055	0.009	1.750 × 10−2
1.810 × 10−1	4.823 × 10−2	8.731 × 10−3	2.040 × 10−2	−1.048	1.099	1.058	0.010	1.818 × 10−2
1.729 × 10−1	5.021 × 10−2	8.682 × 10−3	2.307 × 10−2	−1.050	1.103	1.061	0.011	1.882 × 10−2
1.653 × 10−1	5.207 × 10−2	8.608 × 10−3	2.589 × 10−2	−1.052	1.107	1.064	0.012	1.942 × 10−2
1.581 × 10−1	5.383 × 10−2	8.512 × 10−3	2.884 × 10−2	−1.054	1.111	1.067	0.014	1.997 × 10−2
1.514 × 10−1	5.547 × 10−2	8.398 × 10−3	3.192 × 10−2	−1.055	1.114	1.070	0.015	2.049 × 10−2
1.450 × 10−1	5.699 × 10−2	8.266 × 10−3	3.512 × 10−2	−1.057	1.117	1.073	0.016	2.098 × 10−2
1.390 × 10−1	5.840 × 10−2	8.119 × 10−3	3.844 × 10−2	−1.058	1.120	1.076	0.018	2.143 × 10−2
1.333 × 10−1	5.969 × 10−2	7.959 × 10−3	4.187 × 10−2	−1.060	1.123	1.079	0.020	2.186 × 10−2

,

Table A7. The concentration calculation of ions in mixed solution [M] at equilibrium using K_co and the [SO₄²⁻] at equilibrium calculated (Table A5 and Table A7).

SW	Constant (Equation (13))	[Ba2+]	[Mg2+]	[Ca2+]	[Sr2+]
Mixing Ratio	1 + Kco([SO42−])	[Ba2+] at Equilibrium	[Mg2+] at Equilibium	[Ca2+] at Equilibium	[Sr2+] at Equilibium
0	1.0001	2.67 × 10−4	9.60 × 10−2	2.79 × 10−1	4.98 × 10−3
5	1.0002	2.52 × 10−4	9.44 × 10−2	2.66 × 10−1	4.72 × 10−3
10	1.0004	2.39 × 10−4	9.29 × 10−2	2.53 × 10−1	4.48 × 10−3
15	1.0006	2.27 × 10−4	9.16 × 10−2	2.42 × 10−1	4.27 × 10−3
20	1.0009	2.17 × 10−4	9.04 × 10−2	2.32 × 10−1	4.08 × 10−3
25	1.0011	2.07 × 10−4	8.93 × 10−2	2.23 × 10−1	3.90 × 10−3
30	1.0015	1.98 × 10−4	8.83 × 10−2	2.14 × 10−1	3.74 × 10−3
35	1.0018	1.90 × 10−4	8.73 × 10−2	2.06 × 10−1	3.59 × 10−3
40	1.0023	1.82 × 10−4	8.65 × 10−2	1.99 × 10−1	3.45 × 10−3
45	1.0027	1.75 × 10−4	8.57 × 10−2	1.93 × 10−1	3.32 × 10−3
50	1.0032	1.69 × 10−4	8.49 × 10−2	1.86 × 10−1	3.21 × 10−3
55	1.0037	1.63 × 10−4	8.42 × 10−2	1.81 × 10−1	3.10 × 10−3
60	1.0043	1.57 × 10−4	8.35 × 10−2	1.75 × 10−1	3.00 × 10−3
65	1.0048	1.52 × 10−4	8.29 × 10−2	1.70 × 10−1	2.90 × 10−3
70	1.0055	1.47 × 10−4	8.23 × 10−2	1.66 × 10−1	2.81 × 10−3
75	1.0061	1.42 × 10−4	8.18 × 10−2	1.61 × 10−1	2.73 × 10−3
80	1.0068	1.38 × 10−4	8.13 × 10−2	1.57 × 10−1	2.65 × 10−3
85	1.0075	1.34 × 10−4	8.08 × 10−2	1.53 × 10−1	2.57 × 10−3
90	1.0082	1.30 × 10−4	8.03 × 10−2	1.50 × 10−1	2.50 × 10−3
95	1.0090	1.26 × 10−4	7.98 × 10−2	1.46 × 10−1	2.44 × 10−3
100	1.0098	1.23 × 10−4	7.94 × 10−2	1.43 × 10−1	2.37 × 10−3

,

Table A8. The calculation of the IAP, Ksp, and SI of each BaSO₄ using Equations (16) and (19).

SW	[M2+][SO42−] = IAP	LOG([Ba2+][SO42−])	[BaSO4]	[BaSO4]
Mixing Ratio	[Ba2+][SO42−]	log (IAP) of BaSO4	Pksp	Saturation Index (SI)
0	5.80 × 10−7	−6.2366	6.7541	0.5174
5	1.08 × 10−6	−5.9664	6.7382	0.7718
10	1.47 × 10−6	−5.8315	6.7265	0.8950
15	1.78 × 10−6	−5.7486	6.7182	0.9695
20	2.03 × 10−6	−5.6929	6.7124	1.0195
25	2.22 × 10−6	−5.6537	6.7088	1.0551
30	2.37 × 10−6	−5.6253	6.7069	1.0816
35	2.49 × 10−6	−5.6045	6.7064	1.1019
40	2.57 × 10−6	−5.5892	6.7071	1.1179
45	2.64 × 10−6	−5.5781	6.7087	1.1306
50	2.69 × 10−6	−5.5701	6.7110	1.1409
55	2.72 × 10−6	−5.5647	6.7140	1.1493
60	2.75 × 10−6	−5.5612	6.7175	1.1563
65	2.76 × 10−6	−5.5593	6.7213	1.1621
70	2.76 × 10−6	−5.5587	6.7255	1.1669
75	2.76 × 10−6	−5.5591	6.7300	1.1709
80	2.75 × 10−6	−5.5604	6.7347	1.1743
85	2.74 × 10−6	−5.5624	6.7395	1.1771
90	2.72 × 10−6	−5.5650	6.7444	1.1795
95	2.70 × 10−6	−5.5680	6.7495	1.1814
100	2.68 × 10−6	−5.5715	6.7545	1.1830

and

Table A9. The amount precipitated as in Equation (8) using the molar concentration of Ba²⁺ and SO₄²⁻ at equilibrium and the estimated Ksp.

	Amount	Amount
	Precipitated	Precipitated
Mixing Ratio	mol/L	mg/L
0	0.00018	21
5	0.00021	24
10	0.00021	24
15	0.00020	24
20	0.00020	23
25	0.00019	22
30	0.00018	21
35	0.00018	20
40	0.00017	20
45	0.00016	19
50	0.00016	18
55	0.00015	18
60	0.00015	17
65	0.00014	17
70	0.00014	16
75	0.00013	16
80	0.00013	15
85	0.00013	15
90	0.00012	14
95	0.00012	14
100	0.00012	13

in Appendix B.

Equations (6)–(19) were applied to estimate the saturation index (SI) of five sulfate minerals (SMs) in the mixed solutions [65,70]. A sample of calculations for BaSO₄ mixed with HSBS-3-19 is shown in Table A4, Table A5, Table A6, Table A7, Table A8, Table A9 and

Table A10. The induction time required to precipitate BaSO₄ using the Kan and Masson (2012) correlation [77].

Mixing Ratio	Induction Time	Induction Time
	KAN Equation	KAN Equation
	sec	min
0	73,876,414,107.62	1,231,273,568.46
5	8,127,659.26	135,460.99
10	633,403.88	10,556.73
15	185,416.07	3090.27
20	89,969.12	1499.49
25	56,010.45	933.51
30	40,178.40	669.64
35	31,484.08	524.73
40	26,164.84	436.08
45	22,655.40	377.59
50	20,209.40	336.82
55	18,433.23	307.22
60	17,102.59	285.04
65	16,081.59	268.03
70	15,283.69	254.73
75	14,651.52	244.19
80	14,145.66	235.76
85	13,738.26	228.97
90	13,409.14	223.49
95	13,143.33	219.06
100	12,929.54	215.49

in Appendix B.

The SI values indicate which SMs are likely to precipitate under different operating conditions and thus can be considered for extraction. Figure 1 presents the SI of BaSO₄ when Kuwait seawater was mixed with HSBS-1, HSBS-2, and HSBS-3.

From Figure 1, it is clear that the SI for the three mixed streams is above zero regardless of the mixing ratios, which implies that BaSO₄ minerals can be precipitated directly after mixing, regardless of the type of HSBS mixed with Kuwait seawater. However, HSBS-3-19 shows the lowest potential and lowest SI of BaSO₄ because that stream has the lowest barium concentration among other HSBSs. In contrast, the SI was approximately 0.5 before mixing for HSBSs and increased to 1.0 when mixed with 20% Kuwait SW, further increasing to 1.2 at an 80% mixing ratio. HSBS-1-15 shows the highest potential to precipitate BaSO₄, up to 1.8 SI at 20% mixing, and the SI was then found to decrease as the percentage of SW increased, due to a decrease in the Ba concentration as the % of SW increased. Moreover, the SI for the mixture of HSBS-2-17 and SW was found to be above 1.8 initially and decreased to about 1.7 as the percentage of SW increased to 40%.

Figure 2 shows the quantity of BaSO₄ expected to precipitate at ambient conditions when mixing HSBS-1, -2, and -3 with Kuwait SW; the amount of precipitated minerals was calculated using Equation (8). From Figure 2, it is clear that HSBS-1-15 will precipitate the highest quantity of BaSO₄, up to 75 mg/L at a 20% mixing ratio. This quantity is decreased as the % mixture increases, since the resulting Ba concentration in the mixing stream of HSBS-1-15 and SW will be 82.3 mg/L and decrease as the volume of SW mixed is increased to reach 76.8 mg/L at 90% of mixing.

In contrast, the SO₄²⁻ concentration increased as the volume of seawater increased. That is because Kuwait SW has a high sulfate concentration, while HSBSs have a high barium concentration. Other streams, resulting from HSBS-2-17, HSBS-3-19, and SW, were found to produce a lower quantity of precipitated BaSO₄ when mixed with Kuwait SW due to the lower concentration of barium and sulfate. Figure 1 and Figure 2 demonstrated that barite (BaSO₄) has the highest extraction potential due to its high saturation index, short induction time, and reasonable precipitated quantities at ambient conditions.

3.4. Sulfate Mineral Extraction

Figure 3 shows the SI of CaSO₄·2H₂O (Di-hydrate) (gypsum), which usually precipitates at low operating conditions and salinity for three types of HSBSs when mixed with Kuwait SW at ambient temperature and pressure, and at 200 °C. Figure 3 shows that SI is negative regardless of the type of HSBS used or the quantity of SW used at ambient conditions, which indicates that this mineral tends to dissolve at ambient temperature and pressure, but at high temperatures, such as 200 °C, it was expected to precipitate at the reservoir conditions of high temperature and pressure (Figure 3), which implies high potential for high-purity BaSO₄ precipitated at ambient conditions by only mixing these two streams.

Figure 4 represents the SI of CaSO₄ anhydrous, which is usually stable at high temperatures. Still, when we mixed Kuwait SW with HSBSs, it was found that this type of sulfate scale is precipitated regardless of the mixing ratio, kind of HSBS used, and operating temperature and pressure. The highest potential for extraction was also found for HSBS-1-15, as the highest calcium concentration was detected in that brine solution. In contrast, HSBS-3-19 showed the lowest SI, and the potential for extraction of minerals increased as the percentage of mixing increased, as indicated by the increase in sulfate concentration in the mixture from 610 mg/L to 2212 mg/L, as calculated by the simple model proposed.

Figure 5 displays the SI of the SrSO₄ for the mixture solution using three types of HSBSs: HSBS-1, -2, and -3. HSBS-2-17, followed by HSBS-1-15, exhibited the highest SI, and the lowest SI was noticed when mixing SW with HSBS-1-19 However, SrSO₄ is expected to precipitate regardless of the type of HSBS used or the mixing ratio, referring to the elevated concentration of Sr on that type of HSBS, where the maximum concentration of Sr was displayed at HSBS-2-17.

Figure 6 shows the SI of the five SMs that could precipitate when mixing SW with HSBSs. The figure shows that BaSO₄ has the highest potential to extract, where the SI is 0.5 and increases to 1.20 at 80% mixing, followed by CaSO₄ anhydrous, then SrSO₄, and CaSO₄ hemihydrate. The lowest SI display was for CaSO₄ dihydrate, which shows a negative SI, implying dissolution at all mixing ratios. It also shows that BaSO₄ and CaSO₄ anhydrous consistently precipitate regardless of mixing ratio or operating conditions, while CaSO₄ dihydrate (gypsum) precipitates only at higher temperatures and pressures.

3.5. The Expected Quantity of the SMs Precipitated

Figure 7 illustrates the predicted quantity of CaSO₄ anhydrous precipitated under ambient conditions when Kuwait seawater is mixed with the three HSBS types. The results show a clear increase in precipitation with higher seawater fractions, which is expected since both calcium and sulfate concentrations rise as the mixing ratio increases. According to the proposed model, CaSO₄ anhydrous reaches approximately 800 mg/L at 20% seawater and increases to around 1400 mg/L at 80% seawater (Figure 7). A precipitate level of 800 mg/L can be considered significant, especially when compared to reported values of 2395 mg/L at 105 °C [83]. These findings highlight the potential of extracting CaSO₄ anhydrous, along with SrSO₄ and BaSO₄, by simply mixing disposal brine streams with seawater. The results also suggest that the predicted quantities are feasible for filtration and separation processes. However, the economic feasibility of such extraction depends not only on the amount recovered but also on factors such as the total water volume processed, the purity of the extracted minerals, and the associated separation costs.

A positive saturation index (SI) confirms that the physical separation of a mineral is feasible, particularly when slow crystallization and controlled operating conditions are applied to improve purity and reduce impurities. Three main factors typically influence precipitation and extraction: temperature, pressure, and ionic strength. In this study, ionic strength (I) was identified as the primary factor driving precipitation. Mixing seawater with HSBSs increased the I to approximately 11.0, as predicted by the model, and this rise in ionic strength, combined with higher ion product (IP), served as the main motivated factor for mineral precipitation under ambient conditions. While adjusting operating conditions such as temperature and pressure could further increase extraction yields, doing so would also raise costs. The proposed model offers flexibility to evaluate the influence of temperature and pressure on the SI of selected sulfate minerals and can be extended to other minerals of interest, such as CaCO₃, Mg(OH)₂, and Li₂CO₃. Figure 7 shows that HSBS-3 has the highest potential to precipitate CaSO₄ anhydrous, and a significant amount of CaSO₄ anhydrous is expected to precipitate even though the mixing process is conducted at ambient temperature. This may refer to the highly saturated condition, because of the high concentrations of sulfate and calcium ions in HSBS-1, followed by HSBS- 2 and finally HSBS-3. Furthermore, the high ionic strength of HSBSs play an important role in increasing the saturation degree of SMs when mixing SW which is rich with SO₄²⁻ ions with HSBSs that have a significant amount of Br, Sr, and calcium, in addition to Cl, Na, and Mg, which further increased the ionic strength.

3.6. The Effect of Temperature and Pressure on the Precipitation of SMs

The used model presents a thermodynamic calculated model that could be used to predict SM scaling tendency from mixtures of Kuwait seawater and HSBSs under varying operating pressures and temperatures. Figure 8 presents the relationship between the SI of CaSO₄ anhydrous and the percentage of seawater mixed with HSBS-3-19 under different pressures and temperatures.

The model results show that increasing the mixing ratio raises the SI, indicating greater potential for CaSO₄ anhydrous precipitation. The highest SI values (>5) occurred at 5000 psi and 2000 °C, but the SI dropped to below 3 when the temperature was reduced to 800 °C at the same pressure, highlighting the strong influence of temperature. At atmospheric pressure, only minor SI changes were observed with a temperature increase from 20 to 40 °C. A larger SI increase was recorded when both temperature and pressure were raised, for example, at 5000 psi and 500 °C. At 200 psi, SI values rose from ~1.0 to above 3.0 as the temperature increased from 350 to 600 °C. Conversely, a sharp SI decrease was seen when the temperature fell from 2000 °C to 800 °C (from 5.0 to <1.5), despite constant pressure at 5000 psi. Overall, the results indicate that temperature exerts a stronger effect than pressure on the SI of CaSO₄ anhydrous, though both parameters generally enhance precipitation potential under reservoir-like conditions.

3.7. The Induction Time Required for Precipitation

Figure 9 illustrates the induction time required for the precipitation of CaSO₄ anhydrous, BaSO₄, and SrSO₄ at different mixing ratios. In general, increasing the mixing ratio reduces the induction time for all three minerals. Among them, BaSO₄ shows the shortest induction time, indicating that it precipitates first, followed by CaSO₄ anhydrous, while SrSO₄ requires the longest time. At 30% mixing under ambient conditions, BaSO₄ precipitates in about 400 min, whereas CaSO₄ anhydrous requires more than 1000 min. This suggests that, under practical and economic conditions, BaSO₄ (barite) is the most favorable mineral for extraction before re-injection into the reservoir, due to its high extraction potential, high SI, and short induction time. CaSO₄ anhydrous is the second most viable option, while SrSO₄ is less favorable because of its longer induction period and lower SI. Furthermore, the variation in the induction time increases the potential for easy separation and results in a high percentage of purity in the extracted minerals.

4. Conclusions

The proposed model provides a straightforward yet effective tool for predicting the precipitation potential of sulfate minerals (SMs) under varying temperatures, pressures, mixing ratios, and ionic strengths. Results show that gypsum (CaSO₄·2H₂O) is the only SM unlikely to precipitate under ambient conditions when mixing Kuwait seawater (SW) with HSBSs, though it may precipitate under reservoir conditions at elevated temperature and pressure. In contrast, BaSO₄, SrSO₄, CaSO₄ (anhydrous), and hemihydrate demonstrate strong precipitation potential across different operating conditions. Among them, barite (BaSO₄) exhibits the highest extraction potential, with a saturation index (SI) of up to 1.8, precipitation yields reaching 90 mg/L, and the shortest induction time.

These factors make BaSO₄ especially suitable for recovery immediately after mixing HSBSs with SW, particularly since its solubility decreases at lower temperatures and ambient pressures. Additionally, the time required for CaSO₄ anhydrous to precipitate is longer than that required for barium, especially when the mixing ratio is below 50%.

CaSO₄ anhydrous and SrSO₄, which show reverse solubility behavior, have greater potential for extraction under elevated temperature and pressure but are also predicted to precipitate at ambient conditions, although with longer induction times. Although BaSO₄ records the lowest induction time, the model predicts that CaSO₄ anhydrous may precipitate in larger quantities (over 1000 mg/L), reflecting the high sulfate concentration in SW and calcium levels in HSBSs.

CaSO₄ anhydrous and SrSO₄, which exhibit reverse solubility behavior, have greater potential for extraction under elevated temperature and pressure but are also predicted to precipitate at ambient conditions according to the result of the model with longer induction times. On the other hand, although BaSO₄ shows the lowest induction time, the model predicts that CaSO₄ anhydrous may precipitate in larger quantities (over 1000 mg/L), which is a result of high sulfate concentration in seawater and calcium levels in HSBSs.

Overall, BaSO₄ stands out as the most practical target for extraction due to its high SI, reverse solubility, and short induction period. Furthermore, if the result of the model could be validated through experimental work, that could help reduce scaling risks in reservoirs, improve oil recovery, lower operational costs, and generate valuable mineral byproducts.

The results also confirm that the operating parameters, such as temperature, pressure, mixing ratio, and ionic strength, critically influence the scaling potential and mineral precipitation. The proposed model combined chemical theories (Pitzer, Debye–Hückel) and empirical data, which extends its application to complex, high-ionic-strength reservoir conditions up to 12 M.

Refining the model kinetics, expanding the diversity of brine chemistry, and conducting techno-economic analysis are significant steps to establish the required technology for mineral extraction, which should be integrated with desalination and oil production processes. Finally, critical interpretation and theoretical improvements can impact mineral recovery, brine management, and create new mining prospects.